Problem: If $a+b = 6$ and $a - b = 2$, what is the value of $a^2 - b^2$?
Explanation: Notice that $(a+b) \cdot (a-b) = a^2 + ab - ab - b^2$, which simplifies to $a^2 - b^2$. Substitute $6$ for $a+b$ and $2$ for $a-b$ to find that $a^2 - b^2 = 6 \cdot 2 = \boxed{12}$.